Rep. Anna Eshoo, D-Calif., right, participates in a mock swearing-in ceremony with House Speaker John Boehner, R-Ohio, earlier this year in Washington.
Cloistered in a tense, private Capitol Hill meeting for House Democrats this month, Eshoo had some advice for the aides to President Barack Obama: Stop setting “red lines” that might be broken.

WASHINGTON — A month after emerging from a government shutdown at the top of their game, many Democrats in Congress newly worried about the party’s re-election prospects are for the first time distancing themselves from President Barack Obama after the disastrous rollout of his health care overhaul. At issue, said several Obama allies, is a loss of trust in the president after only 106,000 people — instead of an anticipated half million — were able to buy insurance coverage the first month of the new “Obamacare” websites. In addition, some 4.2 million Americans received notices from insurers that policies Obama had promised they could keep were being canceled.

“Folks are now, I think in talking to members, more cautious with regard to dealing with the president,” said Maryland Rep. Elijah Cummings, the senior Democrat on the House Oversight Committee and one of the first leaders in his state to endorse Obama’s presidential candidacy six year ago.

Cummings, the White House’s biggest defender in a Republican-controlled committee whose agenda is waging war against the administration over Benghazi, the IRS scandal, a gun-tracking operation and now health care, said he still thinks Obama is operating with integrity. But he noted that not all his Democratic colleagues agree.

“They want to make sure that everything possible is being done to, number one, be transparent, (two) fix this website situation and, three, to restore trust,” Cummings said.

Rep. William Lacey Clay, D-Mo., like Cummings, a prominent member of the Congressional Black Caucus who personally likes Obama, struggled to describe the state of play between congressional Democrats and the president.

“I am trying to think if you can call it a relationship at this point,” he said.

Clay said the administration is now obligated to “fix it, fix all of it” after Obama apologized this month for both the insurance website problems and his earlier promises that people could keep their old polices. Otherwise, he said, “a wide brush will be used to paint us all as incompetent and ineffective.”

Obama is now allowing insurance companies to reissue their canceled policies for another year. But “Obamacare’s” problems have left Democrats vulnerable to an orchestrated assault by Republicans who six weeks ago were on the losing end of the government shutdown.

The political body language tells the story of the strain. Thirty-nine House Democrats in Obama’s party defied the president’s veto threat and voted for a GOP-sponsored bill to permit the sale of individual health coverage that falls short of requirements in the law.

“I think people want to have a little more transparency going forward with whoever is implementing the website and other elements,” said Jeff Link, senior adviser to Iowa Rep. Bruce Braley, who is running for Senate and voted for both the original health care law and the GOP-sponsored House bill this month. “If demanding that kind of transparency means lack of trust,” he added delicately, “then I think people probably would like to have had more transparency.”

Across the Capitol, several swing-state Senate Democrats have signed onto legislation to further weaken the health care law. Sponsored by Louisiana Sen. Mary Landrieu, who’s facing a tough re-election challenge, the bill would require insurance companies to permanently continue selling policies that the law deems substandard. Landrieu herself skipped an event with Obama earlier this month when he appeared at the Port of New Orleans. She said she had a long-standing engagement elsewhere in the state, which Obama lost last year by 17 points.

Repairing the relationship between Obama and his allies may be as complex as fixing the website and health care law. Much rests on rebuilding trust with the public, a solid majority of which now opposes “Obamacare,” according to multiple polls. Both parties will be watching Saturday to see whether the vast majority of those who try to sign up for policies on the website will succeed, as Obama has promised. Democrats have urged the administration to quit setting “red lines” like the Nov. 30 deadline, that carry the risk of being broken.

Nearly a year from the midterm election, Republicans in both chambers are launching a drive to link virtually every congressional Democrat to Obamacare. In the House, the effort, based around dozens of votes to repeal the law, is about denying Democrats the 17-seat gain they would need to win back the majority. In the Senate, it’s about gaining the six seats Republicans need to take control of that chamber.

“So you’re running on Obamacare,” read a faux tip sheet from House Republicans to House Democrats that went out over the holiday week. “The best thing to do,” it advises Democratic lawmakers in 28 districts, “is step in front of the cameras and explain to voters why government should run their health care.”

Senate Republicans, meanwhile, showed notable discipline last week when they complained loudly about the Democrats’ new limits on filibusters — then pivoted in as little as one sentence back to “Obamacare.”

The filibuster limits, said Senate Republican Leader Mitch McConnell, can be chalked up to “broken promises, double standards and raw power — the same playbook that got us Obamacare.”

Democratic leaders scoff at the notion that missed deadlines and other problems could threaten the party’s prospects 11 months down the road. A similar budget-and-debt fight that sparked the shutdown and smacked Republicans last month looms early next year, they point out. There is time, they insist, for the law to begin working as intended and to help elevate the Democrats’ political prospects.

“Yesterday’s battles and today’s battles and tomorrow’s battles create different environments,” said House Democratic campaign chief Steve Israel, D-N.Y. Independent voters, the keys to elections in the most competitive districts in the country, are pragmatic, he added. “They want the Affordable Care Act not to be repealed, but to be fixed. They don’t want to go back, they want to go forward.”